The three white metals are different in all ways. Here's a look at how each is used in jewelry and some info you'll need to know when deciding on what to buy.
STERLING SILVER: Sterling silver is the least expensive of the white metals. It's usually stamped "925," which means 92.5% pure silver, and 7.5% other metals. Sterling is used to make neckchains, earrings, rings, bracelets, charms, and anklets. Precious gemstones like diamonds, rubies, emeralds, etc., are rarely, if ever, set in sterling silver. What are commonly set in sterling are the semiprecious stones like onyx, jade, turquoise, and others.
STERLING SILVER PROS: Sterling is very inexpensive and, thus, it's easy to build up a nice collection of pieces of all kinds.
STERLING SILVER CONS: Sterling is relatively soft, it tarnishes, it requires frequent cleaning, and it doesn't offer, in most cases, formal designs. It's a tad more casual, but, in a sense, more fun, because you can buy something for almost every outfit and occasion. Also, some people cannot wear sterling due to metal allergies, especially in the ears. Gold and platinum are essentially hypoallergenic and almost everyone can wear then with no problem. Sterling does cause some people to break out in a rash. (If that happens, remove the jewelry, wash the area with alcohol, and rub a little over-the-counter hydrocortisone cream on the rash and it should clear right up.)
WHITE GOLD: White gold is the most popular "silver" metal. It's used primarily for rings, although you can also find chains, bracelets, and other pieces of jewelry in white gold if you look hard enough, or special order it. White gold is hard, and precious stones are always available in white gold settings. For example, if you're girlfriend, or you yourself if you're of the female denomination, are dying for a ruby ring set in white gold, the odds are you should be able to find one to your liking.
WHITE GOLD PROS: As I said, white gold is hard, which gives it durability, and it holds a mirror shine for a long time.
WHITE GOLD CONS: White gold is considerably more expensive than sterling silver. A plain silver band (like a wedding band design) could cost $10 in sterling and $200 in white gold. Also, because of its cost, if you're the type that likes to wear only one color jewelry - yellow or white - it requires a commitment, especially when it comes to rings. Many women do not like mixing yellow gold and white gold rings on their hands, although this is not carved in stone these days and some people like to mix and match. This is a style decision each person can make for themselves. If you decide on "white only" jewelry, you may find less of a selection due to the overwhelming popularity of yellow gold.
PLATINUM: This is the top of the line when it comes to white metals, and its cost reflects that elevated status. Platinum is very hard, and is commonly used for diamond rings. It is used for other types of jewelry, but because of the wear and abuse rings get on the hands, platinum is commonly chosen by people who want a great deal of longevity in their rings before needing repairs.
PLATINUM PROS: It's the hardest metal used for jewelry, thus providing strength and durability.
PLATINUM CONS: It's expensive, and it turns dull much more quickly than does white gold. Regarding cost, a $200 white gold wedding band could run from $600 and up in platinum.
As is always the case when buying jewelry, price, functionality, and beauty all need to be factored into your buying decision.
If you can wear sterling with no problem, and like a huge collection of earrings or bracelet, or charms, then go for it. You'll find sterling jewelry in the jewelry departments of just about every department store, as well as at jewelers, and online.
If you like the "silver" color but want something of higher quality than sterling, then white gold is the perfect solution.
If you want incredible longevity and durability, and like owning only the best, then platinum is the way to go.
NOTE: Earrings are now available in stainless steel, which is also silver in color, but the bottom line is that stainless is not a precious metal and is commonly chosen by people suffering from severe metal allergies - even to white gold. You almost certainly will not find stainless steel jewelry in a jewelry store, but probably will find stainless steel earrings in department stores.